Recently, Masjed-Jamei and Koepf established the extension of several classical summation theorems (including Gauss’s second summation theorem). Our aim in this paper is to establish a further extension of Gauss’s second summation formulas due to Masjed-Jamei and Koepf in the most general form. The result is then applied to obtain extensions of (i) Knuth’s old sum (or the Reed Dawson identity) and (ii) Riordan’s identity in the most general form. A few interesting results are obtained as special cases of our main findings.
- Knuth's old sum
- Reed Dawson identity
- Riordan identity
- Gauss second summation theorem
- Hypergeometric summation formulas and identities